### On $n$-normed spaces.

Gunawan, Hendra, Mashadi, M. (2001)

International Journal of Mathematics and Mathematical Sciences

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Gunawan, Hendra, Mashadi, M. (2001)

International Journal of Mathematics and Mathematical Sciences

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In this paper, we consider a generalized triangle inequality of the following type: $${\u2225{x}_{1}+\cdots +{x}_{n}\u2225}^{p}\u2a7d\frac{{\u2225{x}_{1}\u2225}^{p}}{{\mu}_{1}}+\cdots +\frac{{\u2225{x}_{2}\u2225}^{p}}{{\mu}_{n}}\left(forall{x}_{1},...,{x}_{n}\in X\right),$$ where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].

Costara, Constantin, Popa, Dumitru (2001)

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